Bøger i Dolciani Mathematical Expositions serien

Describes techniques for solving problems in maxima and minima other than the methods of calculus.

A concise guide to support an undergraduate real analysis course.

A concise but accessible guide to functional analysis that begins with the basics before moving on to more advanced topics.

An accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry.

A collection of 90 short elementary gems from algebra, geometry, combinatorics, and Number Theory.

An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs.

The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman.

A collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.

A beautifully illustrated collection of striking and original results in geometry. Recommended for students and teachers of geometry and calculus.

Offers an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and historical motivation, this is a textbook for a second undergraduate course in number theory.

Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

A guide to the hidden byways of algebra, calculus and geometry, for the seasoned mathematical traveller.